Solve 5x-3/7-2x-1/14-3x-4/5=2x-5/21+frac{3x-4}{10}

$$\frac { 5 x - 3 } { 7 } - \frac { 2 x - 1 } { 14 } - \frac { 3 x - 4 } { 5 } = \frac { 2 x - 5 } { 21 } + \frac { 3 x - 4 } { 10 }$$

Solve for x

$$x = \frac{227}{89} = 2\frac{49}{89} \approx 2.550561798$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 210, the least common multiple of 7,14,5,21,10.

$$30\left(5x-3\right)-15\left(2x-1\right)-42\left(3x-4\right)=10\left(2x-5\right)+21\left(3x-4\right)$$

Use the distributive property to multiply 30 by 5x-3.

$$150x-90-15\left(2x-1\right)-42\left(3x-4\right)=10\left(2x-5\right)+21\left(3x-4\right)$$

Use the distributive property to multiply -15 by 2x-1.

$$150x-90-30x+15-42\left(3x-4\right)=10\left(2x-5\right)+21\left(3x-4\right)$$

Combine 150x and -30x to get 120x.

$$120x-90+15-42\left(3x-4\right)=10\left(2x-5\right)+21\left(3x-4\right)$$

Add -90 and 15 to get -75.

$$120x-75-42\left(3x-4\right)=10\left(2x-5\right)+21\left(3x-4\right)$$

Use the distributive property to multiply -42 by 3x-4.

$$120x-75-126x+168=10\left(2x-5\right)+21\left(3x-4\right)$$

Combine 120x and -126x to get -6x.

$$-6x-75+168=10\left(2x-5\right)+21\left(3x-4\right)$$

Add -75 and 168 to get 93.

$$-6x+93=10\left(2x-5\right)+21\left(3x-4\right)$$

Use the distributive property to multiply 10 by 2x-5.

$$-6x+93=20x-50+21\left(3x-4\right)$$

Use the distributive property to multiply 21 by 3x-4.

$$-6x+93=20x-50+63x-84$$

Combine 20x and 63x to get 83x.

$$-6x+93=83x-50-84$$

Subtract 84 from -50 to get -134.

$$-6x+93=83x-134$$

Subtract 83x from both sides.

$$-6x+93-83x=-134$$

Combine -6x and -83x to get -89x.

$$-89x+93=-134$$

Subtract 93 from both sides.

$$-89x=-134-93$$

Subtract 93 from -134 to get -227.

$$-89x=-227$$

Divide both sides by -89.

$$x=\frac{-227}{-89}$$

Fraction \frac{-227}{-89} can be simplified to \frac{227}{89} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{227}{89}$$